CFA Level I Exam · Capital Investments and Capital Allocation

Payback, Discounted Payback, ROI and Profitability Index

Updated 7 October 2026 · Fact-checked

Payback period is the time needed to recover the initial outlay from cash flows. Discounted payback does the same using present values. Average accounting rate of return divides average net income by average book value. Profitability index is PV of future cash flows ÷ initial outlay; accept if above 1.

Understand Payback, Discounted Payback, ROI and Profitability Index

Capital budgeting asks whether a project is worth its cost. NPV and IRR are the main tools. Payback, discounted payback, average accounting rate of return (AAR) and profitability index (PI) are supporting tools you must know, mainly for their formulas, decision rules and weaknesses.

Payback period is the number of years needed for cumulative cash flows to equal the initial investment. It is simple and shows liquidity risk, but it ignores the time value of money and ignores all cash flows after the payback point. A project can pay back fast and still destroy value.

Discounted payback discounts each cash flow at the required rate of return first, then finds when the cumulative present value equals the outlay. It fixes the time value problem. It still ignores cash flows after the payback point, so it can reject a positive-NPV project if the cutoff is too short. If a project does pay back on a discounted basis, its NPV is positive.

Average accounting rate of return uses accounting profit, not cash flow: average net income ÷ average book value. Average net income is measured after depreciation. The denominator follows the question's definition: it may be average book value, often (initial investment + salvage value) ÷ 2 under straight-line depreciation, or it may be the initial investment. AAR ignores the time value of money, depends on depreciation and accounting choices, and has no objective cutoff tied to value creation.

Profitability index is 1 + NPV ÷ initial outlay, which equals PV of future cash flows ÷ initial outlay. Accept if PI > 1, which is the same as NPV > 0. PI measures value per unit invested, so it is useful under capital rationing. For independent projects it agrees with NPV on accept or reject.

Key formulas to remember

Payback period: Years before full recovery + (unrecovered amount at start of year ÷ cash flow in that year); Assumes cash flows arrive evenly through the recovery year. Uses undiscounted cash flows.
Discounted payback: Same as payback, but use PV of each cash flow = CF ÷ (1 + r)^t; Always longer than or equal to simple payback for positive rates.
Average accounting rate of return: AAR = Average net income ÷ Average book value of investment; Average net income is after depreciation. The denominator follows the question's definition: often (initial investment + salvage value) ÷ 2 under straight-line depreciation, or sometimes the initial investment.
Profitability index: PI = PV of future cash flows ÷ Initial investment = 1 + NPV ÷ Initial investment; Accept if PI > 1; reject if PI < 1. Equivalent to NPV > 0 for a single project.

How to solve Payback, Discounted Payback, ROI and Profitability Index questions

Use this method for any question on these four measures.

1Identify which measure is asked: payback, discounted payback, AAR or PI. Note whether the required return is given.
2List the cash flows by year, with the initial outlay at time 0 as a negative.
3For discounted payback and PI, convert each future cash flow to present value using CF ÷ (1 + r)^t.
4For payback, build a cumulative cash flow column and find the year it turns from negative to positive. Interpolate within that year.
5For AAR, use net income, not cash flow. Compute the average book value as the question defines it.
6For PI, add the PVs of future cash flows and divide by the initial outlay. Compare with 1.
7Apply the decision rule or answer the conceptual point: which cash flows or value does the method ignore?
8Check the answer against the options, which run from smallest to largest, and pick the one that matches.

Quickest way: Cumulative column and PI shortcut

When to use it: Use when cash flows are few (3 to 5 years) and options are numerical.

Write cumulative cash flows in a single running line. Stop when it turns positive.
For PI, if you already know NPV, compute PI = 1 + NPV ÷ outlay. No need to rediscount.
On the BA II Plus, press CF, enter CF0 as negative, enter C01, C02 and so on, then NPV, enter I, CPT. Add the outlay back to get PV of inflows.
Quick eliminate: discounted payback must be longer than payback; PI above 1 means positive NPV.

Common mistakes in Payback, Discounted Payback, ROI and Profitability Index

Saying discounted payback considers all cash flows.
Students link discounting with full valuation like NPV.
Fix: Remember it still ignores cash flows after the payback point. Only NPV and IRR use all cash flows.
Using PV of all cash flows including the outlay in the PI numerator.
Confusion with NPV, which nets the outlay.
Fix: PI numerator is PV of future inflows only. NPV is that minus the outlay.
Computing AAR from cash flows instead of net income.
Capital budgeting questions are mostly cash flow based.
Fix: AAR is an accounting measure. Use net income after depreciation.
Treating PI > 1 as a ranking tool for mutually exclusive projects.
A higher PI looks better.
Fix: For mutually exclusive projects, choose the highest NPV. PI is useful for ranking under capital rationing.
Forgetting to interpolate in the payback year.
Students report the whole year in which cumulative cash flow turns positive.
Fix: Add the fraction: unrecovered balance ÷ that year's cash flow.

Worked examples

Example 1

A project costs €100,000 and generates cash flows of €40,000, €50,000, €40,000 and €30,000 in years 1 to 4. The required return is 10%. What are the payback period and the discounted payback period? Options: A) 2.25 and 2.74 years, B) 2.5 and 3.2 years, C) 3.0 and 3.6 years.

Show the solution

Cumulative cash flows: year 1 = 40,000; year 2 = 90,000; year 3 = 130,000.
Payback occurs in year 3. Unrecovered after year 2 = 10,000. Fraction = 10,000 ÷ 40,000 = 0.25. Payback = 2.25 years.
PVs at 10%: year 1 = 40,000 ÷ 1.10 = 36,363.64; year 2 = 50,000 ÷ 1.21 = 41,322.31; year 3 = 40,000 ÷ 1.331 = 30,052.59; year 4 = 30,000 ÷ 1.4641 = 20,490.40.
Cumulative PV: year 1 = 36,363.64; year 2 = 77,685.95; year 3 = 107,738.54.
Unrecovered after year 2 = 100,000 − 77,685.95 = 22,314.05. Fraction = 22,314.05 ÷ 30,052.59 = 0.74. Discounted payback = 2.74 years.
These values match option A. Discounted payback is longer than payback, as expected.

Answer: A) Payback = 2.25 years and discounted payback = 2.74 years.

Example 2

A project requires an initial outlay of $200,000 and produces PV of future cash flows of $236,000 at the required return. What is the profitability index and what is the decision? Options: A) 0.85, reject; B) 1.18, accept; C) 1.36, accept.

Show the solution

PI = PV of future cash flows ÷ initial investment = 236,000 ÷ 200,000.
PI = 1.18.
Check with NPV: 236,000 − 200,000 = 36,000, positive. PI = 1 + 36,000 ÷ 200,000 = 1.18.
PI > 1, so accept.

Answer: B) PI = 1.18, accept.

Exam tips

Know the one-line weakness of each method: payback ignores time value and later cash flows; discounted payback ignores later cash flows; AAR uses accounting income and ignores time value; PI can mislead on mutually exclusive projects.
PI > 1 is identical to NPV > 0. Use that to eliminate options quickly.
Check whether a question asks for cash flow or net income. AAR uses net income.
If the question gives a payback cutoff, compare to it; a project with positive NPV can still fail the cutoff.
Remember that payback shows liquidity risk. Questions may ask why managers still like it.

Practice questions from Capital Investments and Capital Allocation

Payback, Discounted Payback, ROI and Profitability Index in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Payback, Discounted Payback, ROI and Profitability Index: frequently asked questions

What is the difference between payback and discounted payback?

Payback uses raw cash flows. Discounted payback uses present values at the required return. Discounted payback is longer and accounts for the time value of money, but both ignore cash flows after the payback point.

What is the profitability index decision rule?

Accept the project if PI is greater than 1 and reject it if PI is below 1. This matches the NPV rule, since PI = 1 + NPV ÷ initial outlay.

What are the limitations of average accounting rate of return?

It uses accounting net income rather than cash flow, ignores the time value of money, and depends on depreciation methods. It also has no cutoff tied to value creation.

Which capital budgeting method is best for CFA Level I?

NPV is the most reliable because it uses all cash flows, discounts them, and measures value added directly. The others are supporting tools that you should know for their formulas and weaknesses.